As it happens, some features of the proof from [1]}—on the extremal singular values of random matrices with iid rows—, play a central role in the proof of Theorem REF . We use some ideas from the argument in [1]} to show that if \(X\)  is suitable then \(A\)  acts on sparse vectors almost as if it were a Gaussian matrix (see Theorem REF  for an accurate formulation). At the same time, the argument from [1]} cannot be used to prove a version of Theorem REF  even in the case \(T=S^{n-1}\) , let alone for a general set \(T\) ; there is not enough independence for that proof to work.
